What is Illustration For Calculation of Arithmetic Average

Example : The following table gives the number of children born per family in 735 families. Calculate the average number of children born per family.

Number of children born per family

Number of families

Number of children born per family

Number of families

0

96

7

20

1

108

8

11

2

154

9

6

3

126

10

5

4

95

11

5

5

62

12

1

6

45

13

1

Where

∑fdx = the total of the products of tie deviations from the assumed average and the respective frequencies of the items.

If the deviations are further divided by a common factor and if this factor is represented by i,

X‾ A + (∑fdx / N × i)

The following illustrations would clarify these rules :—

Example

The following data relate to sizes of shoes sold by a store during a given week. Find the average size by the short-cut method—

Size of shoes

pairs

No. of

Size of shoes

No. of pairs

4.5

1

8

95

5

2

8.5

82

5.5

4

9

75

6

5

9.5

44

6.5

15

10

25

7

30

10.5

15

7.5

60

11

4

Solution

Computation of the average size of shoes

Short-cut Method No. 1.

Size of shoes

No. of pairs

Deviations from

the assumed

mean (8)

dx

Totaldeviation(fdx)

4.5

1

—3.5

—3.5

5

2

—3.0

—6.0

5.5

4

—2.5

—10.0

6

5

—2.0

—10.0

6.5

15

—1.5

—22.5

7

30

—1.0

—30.0

7.5

60

—0.5

—30.0

8

95

0

+ 0

8.5

82

+0.5

+41.0

9

75

+1.0

+75.0

9.5

44

+1.5

+66.0

10

25

+2.0

+50.0

10.5

15

+2.5

+37.5

11

4

+3.0

+12.0

N=457 =+169

Applying the short-cut method.

Arithmetic average or X = A +(∑dfx)/N

Where A stands for the assumed average ; ∑dfx for the summation of deviations for the assumed average ; and N for the number of items.We get X = 8 +169.5/457 = 8 + .37 = 8.37 Thus the average size of shoes is 8.37

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